A few years ago, I started trying out some new formative assessment techniques. It has been a journey full of surprises. I’ve learned a lot about what my students think along the way. One of the big surprises was during a unit introducing ratios. I gave my students this exit ticket.
When I made it, I was just trying out the structure and thought it was a little bit of fluff. Then, I saw the results. I gave the assessment about a week into a unit introducing ratio reasoning to my sixth grade class. We had completed lessons on tape diagrams, ratio tables, and double number lines. I expected students to just plop those three representations into the exit ticket without much thought. Instead, I got 3:2, 3 to 2, and 3/2.
I’ve given a lot of thought to why I got these responses. Did the students just key in on the “3” part of the question and not really read the prompt carefully? Did I fail to draw out the connections between tape diagrams, ratio tables, and double number lines enough? I don’t know why I got the responses that I did, but pondering the question of why was important. I started working harder at drawing out the connections between the different representations the next year and the next.
I gave this assessment a few days ago. As I walked around the room, I marked each response with either a green or a pink highlighter. Most of the responses were correct. Those students who got a pink mark, went back through their interactive notebook to find their mistakes and correct them.
I still wonder why some of my students are making this mistake, but feel a little closer to the answer.